EduSahara™ Worksheet

Question 1

1.

A
tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
tower
is found to be
45°
.
If the distance between the point and the foot of the
tower
is
50 m
,
find the height of the
tower
.

(i)

49

m
(ii)

53

m
(iii)

51

m
(iv)

47

m
(v)

50

m

Question 2

2.

If P is the point of observation and the observed object is at point O, which of the following angles represent the angle of elevation ?

(i)

∠b
(ii)

∠e
(iii)

∠d
(iv)

∠c

Question 3

3.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 45° and the angle of elevation of the top of the building is 30°. If the height of the flag staff is 19 m, find the height of the building .

(i)

22.96 m
(ii)

30.96 m
(iii)

28.96 m
(iv)

25.96 m
(v)

20.96 m

Question 4

4.

From the top of a 20 m high building , the angle of elevation of the top of a cable tower is 60° and the angle of depression of its foot is 45°. Find the height of the cable tower.

(i)

54.64 m
(ii)

51.64 m
(iii)

49.64 m
(iv)

59.64 m
(v)

57.64 m

Question 5

5.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 200 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 60° respectively. Find the height of the other temple.

(i)

149.33 m
(ii)

156.33 m
(iii)

133.33 m
(iv)

120.33 m
(v)

119.33 m

Question 6

6.

From the top of a light house which is 65 m high from the sea level, the angles of depression of two ships are 60° and 45°. If one ship is exactly behind the other on the same side of the light house , find the distance between the two ships.

(i)

32.47 m
(ii)

27.47 m
(iii)

30.47 m
(iv)

22.47 m
(v)

24.47 m

Question 7

7.

The upper part of a tree is broken into two parts without being detatched. It makes an angle of 30° with the ground. The top of the tree touches the ground at a distance of 150 m from the foot of the tree . Find the height of the tree before it was broken.

(i)

254.82 m
(ii)

275.82 m
(iii)

259.82 m
(iv)

235.82 m
(v)

281.82 m

Question 8

8.

A
radio tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
radio tower
is found to be
30°
.
If the distance between the point and the top of the
radio tower
is
60 m
,
find the height of the
radio tower
.

(i)

30

m
(ii)

31

m
(iii)

27

m
(iv)

33

m
(v)

29

m

Question 9

9.

A
tower
stands vertically on the ground.

The height of the
tower
is
130

√

2

m
.

The distance between the observation point and its top
is
260

m
.

Find the angle of elevation.

(i)

30°
(ii)

105°
(iii)

75°
(iv)

45°
(v)

60°

Question 10

10.

The angles of depression of two boats from the top of a cliff 60 m high are 45° and 60° respectively. Find the distance between the boats, if the boats are on the same side of the cliff .

(i)

20.36 m
(ii)

30.36 m
(iii)

22.36 m
(iv)

28.36 m
(v)

25.36 m

Question 11

11.

From a point 180 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 60° and 30° respectively. Find the height of the cliff.

(i)

103.93 m
(ii)

79.93 m
(iii)

121.93 m
(iv)

129.93 m
(v)

90.93 m

Question 12

12.

A
chimney
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
chimney
is found to be
60°
.
If the distance between the point and the foot of the
chimney
is
160 m
,
find the distance between
the observation point and the top of the
chimney
.

(i)

317

m
(ii)

322

m
(iii)

321

m
(iv)

320

m
(v)

319

m

Question 13

13.

A man on the top of a vertical observation tower observes a car moving at a uniform speed coming directly towards him. If it takes 19 min for the angle of depression to change from 30° to 45°, how soon after this, will the car reach the observation tower?

(i)

24 min 57 sec
(ii)

26 min 59 sec
(iii)

28 min 60 sec
(iv)

25 min 58 sec
(v)

23 min 55 sec

Question 14

14.

A man in a boat rowing away from a lighthouse 75 m high, takes 2 min to change the angle of elevation of the top of the lighthouse from 60° to 45°. Find the speed of the boat.

(i)

8.26 m/sec
(ii)

2.26 m/sec
(iii)

7.26 m/sec
(iv)

1.26 m/sec
(v)

0.26 m/sec

Question 15

15.

There are two temples one on each bank of a river, just opposite to each other. One of the temples is 130 m high. As observed from the top of this temple, the angles of depression of the top and foot of the other temple are 30° and 45° respectively. Find the width of the river .

(i)

146.00 m
(ii)

127.00 m
(iii)

148.00 m
(iv)

108.00 m
(v)

130.00 m

Question 16

16.

The shadow of a vertical tower BA on a level ground is increased by 45 m, when the altitude of the sun changes from 45° to 30°. Find the height of the tower .

(i)

66.48 m
(ii)

64.48 m
(iii)

56.48 m
(iv)

58.48 m
(v)

61.48 m

Question 17

17.

A boy standing on a vertical cliff in a jungle observes two rest houses in line with him on opposite sides deep in the jungle below. If their angles of depression are 30° and 60° and the distance between them is 125 m , find the height of the cliff.

(i)

59.13 m
(ii)

49.13 m
(iii)

57.13 m
(iv)

51.13 m
(v)

54.13 m

Question 18

18.

Two vertical poles are on either side of a road. A 38 m long ladder is placed between the two poles. When the ladder rests against one pole, it makes an angle of 60° with the pole and when it is turned to rest against another pole, it makes an angle of 45° with the road. Find the width of the road.

(i)

50.87 m
(ii)

42.87 m
(iii)

45.87 m
(iv)

48.87 m
(v)

40.87 m

Question 19

19.

A person, walking 15 m from a point toward a flagpost , observes that its angle of elevation changes from 30° to 45°. Find the height of the flagpost .

(i)

(

15
2

√

3

+

15
2

)

m
(ii)

(

15
2

√

18

+

15
2

√

6

)

m
(iii)

(

45
4

√

2

+

15
4

√

6

)

m
(iv)

225
2

m
(v)

(

2

+

√

3

)

m

Question 20

20.

From a point 80 m away from a vertical cliff, the angles of elevation of the top and the foot of a vertical pillar at the top of the cliff are 45° and 30° respectively. Find the height of the pillar.

(i)

28.81 m
(ii)

38.81 m
(iii)

36.81 m
(iv)

33.81 m
(v)

30.81 m

Question 21

21.

A flag is hoisted at the top of a building . From a point on the ground, the angle of elevation of the top of the flag staff is 60° and the angle of elevation of the top of the building is 30°. If the height of the building is 12 m, find the height of the flag staff .

(i)

21.00 m
(ii)

29.00 m
(iii)

24.00 m
(iv)

27.00 m
(v)

19.00 m

Question 22

22.

An observer 1.3 m tall, is 130 m away from a tower . The angle of elevation of the top of the tower from her eyes is 45°. Find the height of the tower .

(i)

149.30 m
(ii)

158.30 m
(iii)

119.30 m
(iv)

114.30 m
(v)

131.30 m

Question 23

23.

Two boys are on opposite sides of a tower of 190 m height. They measure the angle of elevation of the top of the tower as 45° and 30° respectively. Find the distance between the two boys.

(i)

(

−

2

−

√

3

)

m
(ii)

(

−

72200

)

m
(iii)

(

95

√

6

+

285

√

2

)

m
(iv)

(

190

√

6

+

190

√

18

)

m
(v)

(

190

+

190

√

3

)

m

Question 24

24.

A
radio tower
stands vertically on the ground.
From a point on the ground,
the angle of elevation
of the top of the
radio tower
is found to be
60°
.
If the height of the
radio tower
is
110 m
,
find the distance between
the observation point and the foot of the
radio tower
.

(i)

110
3

m
(ii)

110

m
(iii)

110
3

√

3

m
(iv)

110
3

√

18

m
(v)

55

√

2

m

Question 25

25.

The angles of depression of two boats from the top of a cliff 160 m high are 60° and 45° respectively. Find the distance between the boats, if the boats are on the opposite sides of the cliff .

(i)

252.38 m
(ii)

276.38 m
(iii)

256.38 m
(iv)

244.38 m
(v)

237.38 m

Assignment Key